Maximum likelihood estimation of the forest stem volume from VHF SAR data at the individual tree level

An algorithm based on the exact maximum likelihood (ML) estimator for retrieving the mean stem volume of mature forest stands on relatively flat ground is presented. A VHF-band forest backscatter model at the individual tree level is used to derive the algorithm. The model interprets the tree trunk volume as a random variable and employs a concept of random forest reflection coefficient to characterize fluctuations of radar returns from individual trees. The algorithm is derived under the condition that both the trunk volume and forest reflection coefficient are non-random constant values. Performance (normalized standard deviation and bias) of the algorithm is analyzed by means of Monte-Carlo simulation for various scenarios in terms of statistical distributions for the trunk volume and forest reflection coefficient. It is shown that the algorithm exhibits robustness to the distributions and provides nearly unbiased and accurate stem volume estimation over a wide range of the variances of distributions. A computationally efficient algorithm based on the approximate maximum-likelihood (AML) estimator is also derived. It is shown that the performance of this algorithm is close to that of the ML-based one when the signal-to-noise ratio (SNR) is about 6 dB and perfectly coincides with that for SNRges8 dB. The asymptotic performance of the ML-based algorithm in the infinite SNR limit is numerically evaluated. Simulation results have shown that both of the algorithms almost attain the asymptotic performance at physically realizable SNR.